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Rollout:
Posted By: Daniel Murphy In Response To: Rollout: (DC-Ohio)
Date: Thursday, 21 June 2007, at 8:05 p.m.
If white takes the cube, does he reship on any blotting roll by blue?
Yes. White risks very little (the difference between 9-away Crawford and losing) to gain a lot (the difference between an even match at 4-away all and leading 5-away Crawford).
Suppose White estimates 11/36 hits, winning only 80% of the time thereafter, and ignores his chances of getting a second shot. Then White would win ~25% of the time. White's doubling window opens at about 13.5%, and he's well above that.
No Redouble to 8, Lose -> -9,-1 Crawford, ME = 5.4%
Redouble to 8, Lose -> -9, -0, ME = 0%
No Redouble to 8 , Win -> -5,-5, ME = 50%
Redouble to 8, Win -> -1,-5 Crawford, ME = 84.4%
Risk = 5.4%, Gain = 34.4%, R/(R+G) = 5.4/39.9 = 13.5%
Even if Blue rolls 6-6, after which White, if he hits, only wins about 72% of the time (rollout not shown), White should redouble:
The score (after 0 games) is: White 0, Blue 4 (match to 9 points)
Move number 7: White on roll, cube decision?
White 85
Blue 27 Position ID: 914AAGD2tgEACA Match ID: AgEgAQAAIAAA
• White doubles
Cube decision Rollout cubeless equity -0.5702 (Money: -0.6019) Cubeful equities: 1. Double, take -0.3820 2. Double, pass +1.0000 +1.3820 3. No double -0.4005 -0.0185 Proper cube action: Redouble, take Rollout details
Win W g W bg Lose L g L bg Cubeless Cubeful Player White owns 4-cube 0.2199 0.0000 0.0000 - 0.7801 0.0412 0.0006 -0.5702 -0.4005 Standard error 0.0005 0.0000 0.0000 - 0.0005 0.0015 0.0003 0.0010 0.0014 Player Blue owns 8-cube 0.2272 0.0000 0.0000 - 0.7728 0.2371 0.0002 -0.3820 -0.3820 Standard error 0.0012 0.0000 0.0000 - 0.0012 0.0219 0.0001 0.0044 0.0044 Full cubeful rollout with var.redn. 216 games, Mersenne Twister dice gen. with seed 1062244923 and quasi-random dice Play: 2-ply cubeful prune [world class] keep the first 0 0-ply moves and up to 8 more moves within equity 0.12 Skip pruning for 1-ply moves. Cube: 2-ply cubeful prune [world class]
Another rollout; Blue has played 6-2:
The score (after 0 games) is: White 0, Blue 4 (match to 9 points)
Move number 7: White on roll, cube decision?
White 85
Blue 42 Position ID: 974MAACztw0AQA Match ID: AgEgAQAAIAAA
• White doubles
Cube decision Rollout cubeless equity -0.3281 (Money: -0.3483) Cubeful equities: 1. Double, take +0.0054 2. Double, pass +1.0000 +0.9946 3. No double -0.2015 -0.2068 Proper cube action: Redouble, take Rollout details
Win W g W bg Lose L g L bg Cubeless Cubeful Player White owns 4-cube 0.3248 0.0160 0.0004 - 0.6752 0.0143 0.0000 -0.3281 -0.2015 Standard error 0.0016 0.0039 0.0003 - 0.0016 0.0115 0.0000 0.0066 0.0080 Player Blue owns 8-cube 0.3268 0.0145 0.0005 - 0.6732 0.0793 0.0001 +0.0054 +0.0054 Standard error 0.0022 0.0029 0.0003 - 0.0022 0.0397 0.0000 0.0084 0.0084 Full cubeful rollout with var.redn. 108 games, Mersenne Twister dice gen. with seed 1062244923 and quasi-random dice Play: 2-ply cubeful prune [world class] keep the first 0 0-ply moves and up to 8 more moves within equity 0.12 Skip pruning for 1-ply moves. Cube: 2-ply cubeful prune [world class]
Since White can't be winning all the time after rolling one of his 11/36 = 30.55% hits, he must be winning quite a few games with a second-chance shot.
Another rollout; Blue played 6-2, White redoubled and hits with 4-3:
The score (after 0 games) is: White 0, Blue 4 (match to 9 points)
Move number 9: White on roll, cube decision?
White 85
Blue 42 Position ID: 974MAACztw0AQA Match ID: EwEgAQAAIAAA
• White moves bar/21*/18
Alert: very lucky roll! ( +1.054)
# Ply Move Equity • 1 R bar/21*/18 +0.6892
0.8393 0.0285 0.0002 - 0.1607 0.0015 0.0001 +0.6892 +0.6892 0.0030 0.0028 0.0005 - 0.0030 0.0050 0.0001 0.0060 0.0060 Full cubeful rollout with var.redn. 108 games, Mersenne Twister dice gen. with seed 1062244923 and quasi-random dice Play: 2-ply cubeful prune [world class] keep the first 0 0-ply moves and up to 8 more moves within equity 0.12 Skip pruning for 1-ply moves. Cube: 2-ply cubeful prune [world class] 2 2 bar/21* 4/1 +0.6511 ( -0.0381) 0.8173 0.0448 0.0003 - 0.1827 0.0052 0.0000
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